Secondary battery management system

ABSTRACT

A method and system for managing a battery system. The method including receiving at least one measured characteristic of the battery over a pre-defined time horizon from the at least one sensor, receiving at least one estimated characteristic of the battery from a electrochemical-based battery model based on differential algebraic equations, determining a cost function of a Moving Horizon Estimation based on the at least one measured characteristic and the at least one estimated characteristic, updating the electrochemical-based battery model based on the cost function, estimating at least one state of the at least one battery cell by applying the electrochemical-based battery model, and regulating at least one of charging or discharging of the battery based on the estimation of the at least one state of the at least one battery cell.

CROSS-REFERENCE TO RELATED APPLICATION

This application is continuation of U.S. application Ser. No.15/011,148, filed Jan. 29, 2016, the entire content of which is herebyincorporated by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under ARPA-E Award No.DE-AR0000278 awarded by the U.S. Department of Energy. The U.S.government has certain rights in the invention.

FIELD

The invention generally relates to batteries, and more particularly tomanaging the operation of a battery.

BACKGROUND

Rechargeable lithium batteries are attractive energy storage devices forportable electric and electronic devices and electric andhybrid-electric vehicles because of their high specific energy comparedto other electrochemical energy storage devices. A typical lithium cellcontains a negative electrode, a positive electrode, and a separatorlocated between the negative and positive electrodes. Both electrodescontain active materials that react with lithium reversibly. In somecases, the negative electrode may include lithium metal, which can beelectrochemically dissolved and deposited reversibly. The separatorcontains an electrolyte with a lithium cation, and serves as a physicalbarrier between the electrodes such that none of the electrodes areelectrically connected within the cell.

Typically, during charging, there is generation of electrons at thepositive electrode and consumption of an equal amount of electrons atthe negative electrode. During discharging, opposite reactions occur.

During repeated charge/discharge cycles of the battery undesirable sidereactions occur. These undesirable side reactions result in thereduction of the capacity of the battery to provide and store power.

SUMMARY

Traditional approaches to managing the undesirable side reactions in abattery include limiting the rate of charge/discharge of the battery inan attempt to minimize the undesired effects. These efforts can resultin extended charge times and peak power reduction. Thus, there is a needfor a system and method for the determination of the states andparameters within a secondary battery allowing the battery managementsystem to efficiently regulate the operation of the battery.

A summary of certain embodiments disclosed herein is set forth below. Itshould be understood that these aspects are presented merely to providethe reader with a brief summary of these certain embodiments and thatthese aspects are not intended to limit the scope of this disclosure.Indeed, this disclosure may encompass a variety of aspects that may notbe set forth below.

Embodiments of the disclosure are related to systems and methods formanaging the operation of a battery management system that estimatesvarious states and parameters of a battery using a Moving HorizonEstimation method.

In one embodiment, the disclosure provides a method of managing abattery system. The battery system including at least one battery cell,at least one sensor coupled to the at least one battery cell andconfigured to measure at least one characteristic of the battery cell,and a battery management system coupled to the at least one sensor andincluding a microprocessor and a memory. The method comprisingreceiving, by the battery management system, at least one measuredcharacteristic of the battery over a pre-defined time horizon from theat least one sensor, receiving, by the battery management system, atleast one estimated characteristic of the battery from anelectrochemical-based battery model based on differential algebraicequations, determining, by the battery management system, a costfunction of a Moving Horizon Estimation method based on the at least onemeasured characteristic and the at least one estimated characteristic,updating, by the battery management system, the electrochemical-basedbattery model based on the cost function of the Moving HorizonEstimation Method, estimating, by the battery management system, atleast one state of the at least one battery cell by applying theelectrochemical-based battery model that applies differential algebraicequations to account for physical parameters of a chemical compositionof the at least one battery cell, and regulating, by the batterymanagement system, at least one of charging or discharging of thebattery based on the estimation of the at least one state of the atleast one battery cell.

In another embodiment, the disclosure provides a battery managementsystem. The battery management system comprising a processor and amemory storing instructions. The instructions, when executed by theprocessor, cause the battery management system to receive at least onemeasured characteristic of at least one battery cell over a pre-definedtime horizon from at least one sensor, wherein the at least one batterycell and the at least one sensor are part of a battery system, receiveat least one estimated characteristic of the at least one battery cellfrom a electrochemical-based battery model based on differentialalgebraic equations, determine a cost function of a Moving HorizonEstimation method based on the at least one measured characteristic andthe at least one estimated characteristic, update theelectrochemical-based battery model based on the cost function of theMoving Horizon Estimation Method, estimate at least one state of the atleast one battery cell by applying the electrochemical-based batterymodel that applies differential algebraic equations to account forphysical parameters of a chemical composition of the at least onebattery cell, and regulate at least one of charging or discharging ofthe battery based on the estimation of the at least one state of the atleast one battery cell.

The details of one or more features, aspects, implementations, andadvantages of this disclosure are set forth in the accompanyingdrawings, the detailed description, and the claims below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating a battery system including abattery cell and a battery management system with sensing circuitryincorporated into the battery cell, in accordance with some embodiments.

FIG. 2 is a schematic diagram illustrating another battery systemincluding a battery cell, a battery management system, and sensingcircuitry located external to the battery cell, in accordance with someembodiments.

FIG. 3 is a schematic diagram illustrating a Moving Horizon EstimationFilter, in accordance with some embodiments.

FIG. 4 is a block diagram illustrating the operation of a batterymanagement system, in accordance with some embodiments.

FIG. 5 is a block diagram illustrating the operation of another batterymanagement system, in accordance with some embodiments.

DETAILED DESCRIPTION

One or more specific embodiments will be described below. Variousmodifications to the described embodiments will be readily apparent tothose skilled in the art, and the general principles defined herein maybe applied to other embodiments and applications without departing fromthe spirit and scope of the described embodiments. Thus, the describedembodiments are not limited to the embodiments shown, but are to beaccorded the widest scope consistent with the principles and featuresdisclosed herein.

An embodiment of a battery system 100A is shown in FIG. 1. The batterysystem 100A includes a battery cell 102A, an anode tab 110, an anode120, a separator 130, a cathode 150, a cathode tab 160, sensingcircuitry 170A, and a battery management system 180. In some examples,the separator 130 may be an electrically insulating separator. In someembodiments, the electrically insulating separator comprises a porouspolymeric film. In various embodiments the thickness dimension of thecomponents of the battery cell 102A may be for the anode 120 about 5 toabout 110 micrometers, for the separator 130 less than about 50micrometers or in certain embodiments less than about 10 micrometers,and for the cathode 150 about 50 to about 110 micrometers.

During the discharge of battery cell 102A, lithium is oxidized at theanode 120 to form a lithium ion. The lithium ion migrates through theseparator 130 of the battery cell 102A to the cathode 150. Duringcharging the lithium ions return to the anode 120 and are reduced tolithium. The lithium may be deposited as lithium metal on the anode 120in the case of a lithium anode 120 or inserted into the host structurein the case of an insertion material anode 120, such as graphite, andthe process is repeated with subsequent charge and discharge cycles. Inthe case of a graphitic or other Li-insertion electrode, the lithiumcations are combined with electrons and the host material (e.g.,graphite), resulting in an increase in the degree of lithiation, or“state of charge” of the host material. For example, x Li⁺+xe⁻+C₆→Li_(x)C₆.

The anode 120 may comprise an oxidizable metal, such as lithium or aninsertion material that can insert Li or some other ion (e.g., Na, Mg,or other suitable ion). The cathode 150 may comprise various materialssuch as sulfur or sulfur-containing materials (e.g.,polyacrylonitrile-sulfur composites (PAN-S composites), lithium sulfide(Li₂S)); vanadium oxides (e.g., vanadium pentoxide (V₂O₅)); metalfluorides (e.g., fluorides of titanium, vanadium, iron, cobalt, bismuth,copper and combinations thereof); lithium-insertion materials (e.g.,lithium nickel manganese cobalt oxide (NMC), lithium-rich NMC, lithiumnickel manganese oxide (LiNi_(0.5)Mn_(1.5)O₄)); lithium transition metaloxides (e.g., lithium cobalt oxide (LiCoO₂), lithium manganese oxide(LiMn₂O₄), lithium nickel cobalt aluminum oxide (NCA), and combinationsthereof); lithium phosphates (e.g., lithium iron phosphate (LiFePO₄)).

The particles may further be suspended in a porous, electricallyconductive matrix that includes polymeric binder and electronicallyconductive material such as carbon (carbon black, graphite, carbonfiber, etc.). In some examples, the cathode may comprise an electricallyconductive material having a porosity of greater than 80% to allow theformation and deposition/storage of oxidation products such as lithiumperoxide (Li₂O₂) or lithium sulfide, (Li₂S) in the cathode volume. Theability to deposit the oxidation product directly determines the maximumpower obtainable from the battery cell. Materials which provide theneeded porosity include carbon black, graphite, carbon fibers, carbonnanotubes, and other non-carbon materials. The pores of the cathode 150,separator 130, and anode 120 are filled with an ionically conductiveelectrolyte that contains a salt such as lithium hexafluorophosphate(LiPF₆) that provides the electrolyte with an adequate conductivitywhich reduces the internal electrical resistance of the battery cell.The electrolyte solution enhances ionic transport within the batterycell. Various types of electrolyte solutions are available including,non-aqueous liquid electrolytes, ionic liquids, solid polymers,glass-ceramic electrolytes, and other suitable electrolyte solutions.

The separator 130 may comprise one or more electrically insulating ionicconductive materials. In some examples, the suitable materials forseparator 130 may include porous polymers, ceramics, and two dimensionalsheet structures such as graphene, boron nitride, and dichalcogenides.In certain examples the pores of the separator 130 may be filled with anionically conductive electrolyte that contains a lithium salt such aslithium hexafluorophosphate (LiPF₆) that provides the electrolyte withan adequate conductivity which reduces the internal electricalresistance of the battery cell.

The battery management system 180 is communicatively connected to thebattery cell 102A. In one example, the battery management system 180 iselectrically connected to the battery cell 102A via electrical links(e.g., wires). In another example, the battery management system 180 maybe wirelessly connected to the battery cell 102A via a wirelesscommunication network. The battery management system 180 may be forexample a microcontroller (with memory and input/output components on asingle chip or within a single housing) or may include separatelyconfigured components, for example, a microprocessor, memory, andinput/output components. The battery management system 180 may also beimplemented using other components or combinations of componentsincluding, for example, a digital signal processor (DSP), an applicationspecific integrated circuit (ASIC), a field-programmable gate array(FPGA), or other circuitry. Depending on the desired configuration, theprocessor may include one more levels of caching, such as a level cachememory, one or more processor cores, and registers. The exampleprocessor core may include an arithmetic logic unit (ALU), a floatingpoint unit (FPU), or any combination thereof. The battery managementsystem 180 may also include a user interface, a communication interface,and other computer implemented devices for performing features notdefined herein may be incorporated into the system. In some examples,the battery management system 180 may include other computer implementeddevices such as a communication interface, a user interface, a networkcommunication link, and an interface bus for facilitating communicationbetween various interface devices, computing implemented devices, andone or more peripheral interfaces to the microprocessor.

The memory of the battery management system 180 may includecomputer-readable instructions that, when executed by the electronicprocessor of the battery management system 180, cause the batterymanagement system and, more particularly the electronic processor, toperform or control the performance of various functions or methodsattributed to battery management system 180 herein (e.g., calculate astate or parameter of the battery system, regulate the operation of thebattery system, detect an internal short from a dendrite formation). Thememory may include any transitory, non-transitory, volatile,non-volatile, magnetic, optical, or electrical media, such as a randomaccess memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM),electrically-erasable programmable ROM (EEPROM), flash memory, or anyother digital or analog media. The functions attributed to the batterymanagement system 180 herein may be embodied as software, firmware,hardware or any combination thereof. In one example, the batterymanagement system 180 may be embedded in a computing device and thesensing circuity 170A is configured to communicate with the batterymanagement system 180 of the computing device external to the batterycell 102A. In this example, the sensing circuitry 170A is configured tohave wireless and/or wired communication with the battery managementsystem 180. For example, the sensing circuitry 170A and the batterymanagement system 180 of the external device are configured tocommunicate with each other via a network. In yet another example, thebattery management system 180 is remotely located on a server and thesensing circuitry 170A is configured to transmit data of the batterycell 102A to the battery management system 180. In the above examples,the battery management system 180 is configured to receive the data andsend the data to an electronic device for display as human readableformat. The computing device may be a cellular phone, a tablet, apersonal digital assistant (PDA), a laptop, a computer, a wearabledevice, or other suitable computing device. The network may be a cloudcomputing network, a server, a wireless area network (WAN), a local areanetwork (LAN), an in-vehicle network, a cloud computing network, orother suitable network.

The battery management system 180 is configured to receive data from thesensing circuitry 170A including, for example, current, voltage, and/orresistance measurements. The sensing circuitry 170A may include one ormore sensors. Each sensor of the sensing circuitry 170A may measure oneor more characteristics (e.g., a current, a voltage, a resistance,and/or a temperature) of the battery cell 102A. The sensing circuitry170A may be located internal to the battery cell 102A. Batterymanagement system 180 is also configured to determine a condition of thebattery cell 102A (e.g., state-of-charge (SOC) and/or state-of-health(SOH)). Based on the determined condition of battery cell 102A, thebattery management system 180 may alter the operating parameters of thebattery cell 102A to maintain the internal structure of the battery cell102A. The battery management system 180 may also notify a user of thecondition of the battery cell 102A.

Another embodiment of a battery system 100B is shown in FIG. 2. FIG. 2is identical to the FIG. 1, except, as illustrated in FIG. 2, thesensing circuitry 170B can be coupled externally to the battery cell102B via the anode tab 110B and the cathode tab 160B.

In some embodiments the battery cell 102B is part of a closed system. Ina closed system, after the battery cell 102B is produced, the casingthat surrounds the battery cell 102B is sealed to prevent externalelements, such as air and moisture, from entering the battery cell 102Band potentially causing degradation of the battery cell 102B resultingin reduced performance and shorter life of the battery cell 102B.

However, a closed battery cell 102B presents various challenges to thebattery management system 180. The closed system does not allow thedirect observation of the condition of the components of the batterycell 102B. Instead, the sensing circuitry 170B monitors and/or measurescharacteristics (e.g. voltage, current, resistance, power, temperatureand/or combinations thereof) of the battery cell 102B while the batterycell 102B is operating or at rest. The sensing circuitry 170B cantransmit the one or more measured characteristics to the batterymanagement system 180, and the battery management system 180 can receivethe one or more measured characteristics and determine the condition ofthe battery cell 102B based at least in part on the one or more measuredcharacteristics.

Various models have been developed to model the electrochemicalreactions occurring within the battery cell 102B. One example, wasdeveloped by Fuller, Doyle, and Newman, the (Newman Model), (J.Electrochem. Soc., Vol. 141, No. 1, January 1994, pp. 1-10), thecontents of which are hereby incorporated by reference in theirentirety. The Newman Model provides a mathematical model which can beused to estimate the electrochemical processes occurring within thebattery cell 102B based on the measured characteristics.

The charge transfer reactions at the anode 120, and cathode 150, may bemodelled by an electrochemical model, such as the Newman Model,providing the basis to describe various battery cell 102B parametersduring both the charging and discharging of the battery cell 102B. Forexample, the Newman Model may allow the estimation of various parametersincluding cathode particle radius, which can vary due to the degree oflithiation of the cathode 150, which also may be called thestate-of-charge of the battery cell 102B, anode particle radius, iondiffusion rates in the anode 120, cathode 150, and electrolyte,intercalation current and transference number, solution conductivity inthe anode 120, cathode 150, and electrolyte, cell porosity of the anode120 and cathode 150, and equilibrium potential of the anode 120 andcathode 150.

Physics based electrochemical models, such as the Newman Model, mayinclude ordinary and partial differential equations (PDEs) to describethe behavior of the various parameters within the battery cell 102B. TheNewman Model is an electrochemical-based model of the actual chemicaland electrical processes occurring in the Li-ion batteries. However, thefull Newman Model is extremely complex and requires a large number ofimmeasurable physical parameters to be identified. Identification ofsuch large set of parameters involved in the nonlinear PDE anddifferential algebraic equations (DAEs) with current computationalcapacity is impractical. This gives rise to various electrochemicalmodels that approximate the dynamics of the Newman Model.

For example, the Reduced-Order-Model (ROM), Mayhew, C.; Wei He; Kroener,C.; Klein, R.; Chaturvedi, N.; Kojic, A., “Investigation ofprojection-based model-reduction techniques for solid-phase diffusion inLi-ion batteries,” American Control Conference (ACC), 2014, pp. 123-128,4-6 Jun. 2014, the contents of which are hereby incorporated byreference in their entirety, allows the model order reduction of theNewman Model of Li-ion cells while retaining the complete modelstructure of the of the baseline cell. The ROM of the Newman Model isable to accurately predict behavior of a truth model, compared to lessrealistic approximate models such as Single Particle Model, whilereducing computation time and memory requirements. The Newman Modelreduction by ROM, introduces a large number of states and parametersinvolved in highly nonlinear partial differential equations anddifferential algebraic equations of the ROM dynamical system. Thiscontributes to the complexity of the parameter and state identificationprocess. Herein we describe methods of parameter and state estimationfor the highly nonlinear and complex ROM. These methods are based ononline reception of measurement data and achieve a high speed ofestimation.

FIG. 3 illustrates an embodiment of the basic functioning of a MovingHorizon Estimation method (MHE). Moving Horizon Estimation (MHE) methodis a model predictive estimator which can be used by a controller (e.g.,a controller that operates as a battery management system) to solve anopen-loop control problem by using the current states and parameters ofthe modeled system as the initial states of the modeled system at thenext discrete time interval. Predictive estimators, such as the MovingHorizon Estimation (MHE) method, use a moving window of the most recentinformation and carry over the last estimate to the next time instant.MHE uses a series of continuously sampled measurements over time toestimate the states and parameters of the system. The measurements maycontain noise in addition to the measurement. The states, parameters,and noise may be estimated by solving the mathematical model within aset of constraints.

As illustrated in FIG. 3, an actual measured characteristic of thebattery cell 102B is represented as 310. An estimate of thecharacteristic of the battery cell 102B is represented as 320. The MHEmethod seeks to minimize the difference (error) 330 between theestimated value of the characteristic and the actual measured value ofthe characteristic over a series of discrete time measurements 340collected over a predetermined time horizon. That is, a cost function ofthe MHE method is composed of the deviation of the estimated output(e.g., an error between the measured characteristic and the estimatedcharacteristic) from the measured output and an arrival cost thatassumes a weight on the previously estimated states and parameters.

The arrival cost summarizes the effect of the previously measured andestimated data on the current estimation. For a linear unconstrainedsystem or systems, a Kalman Filter covariance update formula can computethe arrival cost explicitly. However, a non-linear unconstrained systemcan be linearized at the currently estimated point and removing theconstraints, and then the Kalman Filter can be employed to theapproximated system. This application of the Kalman Filter to theapproximated system is defined as an Extended Kalman Filter (EKF).

To apply the MHE method to the ROM dynamical system, a batterymanagement system (e.g., the battery management system 180 as describedabove) can determine a time varying arrival cost gain for each parameterbased on its estimation robustness. Additionally, the battery managementsystem can characterize the effect of parameters identifiability in theestimation process and suspension of estimation under low excitation.

To determine a time varying arrival cost gain for each parameter, thebattery management system can use a modified Extended Kalman Filter(EKF) method. In the implementation of EKF in an arrival cost of the MHEmethod, the battery management system may assume that the probabilitydensity functions of the noises in states, parameters and output areshape invariant Gaussian distributions, that is, Gaussian distributionswith time-invariant covariance matrices. However, battery cells undergovarying discharge, charge, and idle operations during relatively shorttime periods as the vehicle accelerates, decelerates, and stops duringoperation. From simulation and empirical data, different parameters andstates of the Reduced Order Model (ROM) of Li-ion battery have differentnoise levels and different influence on the output and their noise andinfluence levels depend on the battery's state of operation.Accordingly, the battery management system may assume that the noisecovariance matrix in estimation of states and parameters is atime-varying matrix that depends on the sensitivity of output on statesand parameters at each horizon. Thus, the battery management system mayemploy different notions of states and parameters' sensitivity such aspartial derivatives of output versus states and parameters andvariations in the output over one drive cycle due to perturbation instates and parameters.

Additionally, the battery management system may also define a directrelation between noise covariance matrix and the sensitivity of outputon parameters and states. The noise covariance matrix has an inverserelation with the arrival cost gains. For example, if the sensitivity ofa parameter or state is gradually decreasing over a drive cycle, thenthe entries in the noise covariance matrix associated with thatparameter or state will also decrease which results in an increase inthe associated arrival cost gain. If the arrival cost gain increasesthen the rate of change in that parameter or state during the predictionphase decreases and hence the parameter or state will have a highertendency to retain its current value. The battery management system mayuse this inverse relationship to create an automatic estimationsuspension mechanism which smoothly takes the focus away from theestimation of one or more parameters and/or states.

To identify states and parameters, the battery management system mayemploy various methods. For example, the battery management systemsuspends the estimation process, that is, the battery management systemsets the parameters equal to the last identified values and predictedthe states according to the system dynamics under a low inputpersistency of excitation. In this example, the battery managementsystem may define an input persistency of excitation to be anintegration of a power gain of a current over the estimation timehorizon. In another example, the battery management system may suspendthe estimation of one or more parameters under low gradient of output orstates function versus those parameters.

An example of an MHE is illustrated in FIG. 4. FIG. 4 is a block diagramillustrating the management of a battery system 400, in accordance withsome embodiments. In the example of FIG. 4, the battery system 400includes a battery 410 and a battery management system 412. The batterymanagement system 412 includes a battery estimator 420, buffers 425A,425B, 425C, noise covariance matrix 430, arrival cost 440, errorevaluation 450, threshold determination 455, a model updater 460,estimate modifier 470, and time interval advancement 480.

A MHE method can be applied to various physical, mathematical, andelectrochemical models of a battery 410. At the first time step, thebattery management system 412 receives at least one measuredcharacteristic (e.g., voltage and/or current) of the battery 410 over apre-defined time horizon from at least one sensor (i.e., thecharacteristics of the battery 410 are sampled) at buffer 425A and 425C.At the first time step, the battery management system 412 also receivesat least one estimated characteristic (e.g., an initial estimate of thestates and parameters of the battery model 420) based on the previoustime interval from battery model 420. The previous time interval isdefined as part of the time interval advancement 480. The at least oneestimated characteristic is provided to buffer 425B. An initial estimateof the noise covariance matrix 430 is generated for these states andparameters. For the first time step there is no data from the previoustime step of the series to act as initial conditions. An initialestimate of the states and parameters is generated from the batterymodel 420 based on values not of this time series (e.g., historicaloperation or manufacturers specifications).

A representation of the states and parameters of the battery 410 and thecorresponding states and parameters from the battery model 420 isprovided in Equations 1 and 2 respectively.

{dot over (x)}(t)=f(x(t),θ,I(t))

0=g(x(t),θ,I(t))

V(t)=h(x(t),θI(t))  (1)

{circumflex over ({dot over (x)})}(t)=f({circumflex over(x)}(t),{circumflex over (θ)},I(t))

0=g({circumflex over (x)}(t),{circumflex over (θ)},I(t))

{circumflex over (V)}(t)=h({circumflex over (x)}(t),{circumflex over(θ)},I(t))  (2)

In Equations 1 and 2, x represents the states, θ represents theparameters, I represents the current inputs, and V represents theoutputs. The Jacobian of the system with respect to the states andparameters is derived based on the partial derivatives of Equation 2 asshown in Equation 3 and the noise covariance matrix 430 is then updatedfor the current time step.

$\begin{matrix}{\frac{\partial f}{\partial\hat{x}},\frac{\partial g}{\partial\hat{x}},\frac{\partial h}{\partial\hat{x}},\frac{\partial f}{\partial\hat{\theta}},\frac{\partial g}{\partial\hat{\theta}},\frac{\partial h}{\partial\hat{\theta}}} & (3) \\{{{COV}\left( {t + 1} \right)} = \left( {{{J_{f}(t)}{{COV}(t)}{J_{f}(t)}^{T}} + {Q(t)} - {{J_{f}(t)}{{COV}(t)}{J_{h}(t)}^{T}\left( {{R(t)} + {{J_{h}(t)}{{COV}(t)}{J_{h}(t)}^{T}}} \right){J_{h}(t)}{{COV}(t)}{J_{f}(t)}^{T}}} \right)} & (4)\end{matrix}$

In Equation 4, COV(t+1) is the covariance at t+1, J_(f) is the Jacobianof f, J^(T) _(f) is the transpose of the Jacobian of f, J_(h) is theJacobian of h, J^(T) _(h) is the transpose of the Jacobian of h, COV(t)is the covariance at t, Q(t) is a noise covariance matrix associatedwith the states and parameters, and R(t) is a noise covariance matrixassociated with the outputs.

The noise covariance matrix 430 of the estimation of states andparameters is calculated from the battery model 420 with the noisecontributions assumed to be time invariant over the measurement horizon.The noise covariance matrix 430 may additionally depend on thesensitivity of the output on the states and the parameters at eachhorizon. In order to capture the contribution of data as the timehorizon is advanced an arrival cost 440 is determined by the batterymanagement system 412. In some embodiments, the arrival cost 440 may bedetermined by the battery management system 412 using an Extended KalmanFilter approach based on the at least one measured characteristic andthe at least one estimated characteristic of the battery 410. In someembodiments, the Kalman Filter gain is inversely related to the arrivalcost.

To implement the Extended Kalman Filter approach, the battery managementsystem 412 determines a cost function of the Moving Horizon Estimationmethod based on the at least one measured characteristic and the atleast one estimated characteristic. For example, the battery managementsystem 412 uses the error evaluation module 450 to generate an amount oferror present for each element of the data set by comparing the measuredcharacteristics of the battery 410 with the estimated characteristics(e.g., the states) of the battery model 420. Further, the batterymanagement system 412 uses the threshold determination 455 to comparethe error between each measured and estimated parameter or state to apredetermined threshold.

If the battery management system 412 determines that the amount of erroris less than a predetermined threshold, then the accuracy of the batterymodel 420 is verified, and the battery management system 412 updates thestates and parameters of the battery model 420 using the model updater460. The updated states and parameters of the battery model 420 act asthe initial states for the next iteration and the time step is advanced(e.g., t=t+1) with time interval advancement 480.

If the battery management system 412 determines that the amount of erroris greater than a predetermined threshold, the accuracy of the batterymodel 420 is not verified, and the battery management system 412modifies the states and parameters of the battery model 420 using theestimate modifier 470. The estimation process of the battery managementsystem 412 is reevaluated until the battery model 420 is verified asaccurate and updated by the battery management system 412.

After updating the battery model 420, the battery management system 412estimates at least one state of the battery 410 by applying theelectrochemical-based model of the battery model 420. In the example ofFIG. 4, the estimation of the at least one state may include estimationof the state-of-charge (SOH) and/or the state-of-health (SOH) of thebattery 410 synchronously. While the estimation of SOC and SOH isperformed synchronously the gains associated with the noise covariancematrices of the states and parameters may be developed together orseparately. Further, after estimating the at least one state, thebattery management system 412 regulates at least one of charging ordischarging of the battery 410 based on the estimation of the at leastone state of the battery 410.

FIG. 5 is a block diagram illustrating the operation of another batterymanagement system 512, in accordance with some embodiments. The system500 of FIG. 5 is identical to the system 400 of FIG. 4 except thebattery management system 512 evaluates states separately. For example,the battery management system 512 determines a cost function associatedwith the state-of-health at the state-of-health evaluation 452.Similarly, the battery management system 512 determines a cost functionassociated with the state-of-charge at the state-of-charge evaluation454. In the example of FIG. 5, the battery management system 512evaluates the states and parameters asynchronously according to thedifference in the time scale associated with the states and parameters.For slowly varying parameters (e.g., state-of-health), the batterymanagement system 512 evaluates the parameters at a pre-defined time.For example, the pre-defined time is once every 10, 25, 50, 100, 150,200, or more than 200 cycles (e.g., drive cycles of a vehicle) comparedto a state (e.g., state-of-charge) that may be evaluated every second,each cycle, or other suitable time period. For rapidly varyingparameters (e.g., state-of-charge), the battery management system 512evaluates the parameters continuously.

The set of outputs from the electrochemical model via the MHE includeevaluations of both rapidly varying states of the battery cell 102B andevaluations of slowly varying parameters of the battery cell 102B. Insome embodiments the state of the battery cell 102B in combination withthe present input to the mathematical model allows the model to predictthe present output of the battery cell 102B. States of a battery cellmay for example include the state-of charge, for a lithium battery thedegree of lithiation, or the hysteresis levels of the battery.Parameters of the battery cell 102B are typically more slowly varyingover time than the states of the battery cell 102B. Additionally, aparameter may not be required for the model to predict the presentoutput of the battery cell 102B. Instead knowledge of the parameters ofbattery cell 102B, which may be called the state-of-health of thebattery, relate to the long term functioning of the battery cell 102B.For example, the functioning of the battery cell 102B over one or morecharge/discharge cycles. Additionally, some embodiments compriseparameters which are not directly determinable from the measurement ofthe current battery cell 102B characteristics. Examples of battery cell102B parameters include the maximum power capacity, maximum poweroutput, and internal resistance.

The embodiments described above have been shown by way of example, andit should be understood that these embodiments may be susceptible tovarious modifications and alternative forms. It should be furtherunderstood that the claims are not intended to be limited to theparticular forms disclosed, but rather to cover all modifications,equivalents, and alternatives falling with the spirit and scope of thisdisclosure.

It is believed that embodiments described herein and many of theirattendant advantages will be understood by the foregoing description,and it will be apparent that various changes may be made in the form,construction and arrangement of the components without departing fromthe disclosed subject matter or without sacrificing all of its materialadvantages. The form described is merely explanatory, and it is theintention of the following claims to encompass and include such changes.

While the invention has been described with reference to variousembodiments, it will be understood that these embodiments areillustrative and that the scope of the disclosure is not limited tothem. Many variations, modifications, additions, and improvements arepossible. More generally, embodiments in accordance with the inventionhave been described in the context or particular embodiments.Functionality may be separated or combined in blocks differently invarious embodiments of the disclosure or described with differentterminology. These and other variations, modifications, additions, andimprovements may fall within the scope of the disclosure as defined inthe claims that follow.

What is claimed is:
 1. A method of managing a battery system, thebattery system including at least one battery cell, at least one sensorcoupled to the at least one battery cell and configured to measure atleast one characteristic of the battery cell, and a battery managementsystem coupled to the at least one sensor and including a microprocessorand a memory, the method comprising: receiving, by the batterymanagement system, at least one measured characteristic of the batteryover a pre-defined time horizon from the at least one sensor; receiving,by the battery management system, at least one estimated characteristicof the battery from a electrochemical-based battery model based ondifferential algebraic equations; determining, by the battery managementsystem, a cost function of a Moving Horizon Estimation method based onthe at least one measured characteristic and the at least one estimatedcharacteristic; updating, by the battery management system, theelectrochemical-based battery model based on the cost function of theMoving Horizon Estimation; estimating, by the battery management system,at least one state of the at least one battery cell by applying theelectrochemical-based battery model that applies differential algebraicequations to account for physical parameters of a chemical compositionof the at least one battery cell; and regulating, by the batterymanagement system, at least one of charging or discharging of thebattery based on the estimation of the at least one state of the atleast one battery cell.
 2. The method of claim 1, wherein determiningthe cost function of the Moving Horizon Estimation method includesdetermining an error between the at least one measured characteristicand the at least one estimated characteristic; and determining anarrival cost that has a weight based on previously estimated states andparameters.
 3. The method of claim 2, wherein determining the arrivalcost includes determining the arrival cost using a Kalman Filter whenthe battery system is a linear unconstrained system.
 4. The method ofclaim 2, wherein determining the arrival cost includes linearizing thebattery system when the battery system is a non-linear constrainedsystem; and determining a time varying arrival cost gain for eachparameter based on a estimation robustness of each parameter using amodified extended Kalman Filter.
 5. The method of claim 1, wherein theat least one state of the at least one battery cell includes at leastone of a state-of-charge or a state-of-health of the at least onebattery cell.
 6. The method of claim 5, wherein estimating the at leastone state of the at least one battery cell by applying theelectrochemical-based battery model includes synchronously estimatingthe state-of-charge and the state-of-health of the at least one batterycell.
 7. The method of claim 5, wherein estimating the at least onestate of the at least one battery cell by applying theelectrochemical-based battery model includes separately estimating thestate-of-charge and the state-of-health of the at least one batterycell, wherein the state-of-charge of the at least one battery cell isestimated continuously, and wherein the state-of-health of the at leastone battery cell is estimated at a pre-defined time.
 8. The method ofclaim 7, wherein the pre-defined time is one hundred drive cycles. 9.The method of claim 1, further comprising suspending the estimation ofthe at least one state of the at least one battery cell under a lowinput persistency of excitation or under a low gradient of output. 10.The method of claim 1, wherein the electrochemical-based battery modelis a Reduced-Order-Model of a Newman model.
 11. A battery managementsystem comprising a processor and a memory storing instructions that,when executed by the processor, cause the battery management system to:receive at least one measured characteristic of at least one batterycell over a pre-defined time horizon from at least one sensor, whereinthe at least one battery cell and the at least one sensor are part of abattery system; receive at least one estimated characteristic of the atleast one battery cell from a electrochemical-based battery model basedon differential algebraic equations; determine a cost function of aMoving Horizon Estimation based on the at least one measuredcharacteristic and the at least one estimated characteristic; update theelectrochemical-based battery model based on the cost function of theMoving Horizon Estimation; estimate at least one state of the at leastone battery cell by applying the electrochemical-based battery modelthat applies differential algebraic equations to account for physicalparameters of a chemical composition of the at least one battery cell;and regulate at least one of charging or discharging of the batterybased on the estimation of the at least one state of the at least onebattery cell.
 12. The battery management system of claim 11, whereindetermine the cost function of the Moving Horizon Estimation includesinstructions that, when executed by the processor, cause the batterymanagement system to determine an error between the at least onemeasured characteristic and the at least one estimated characteristic;and determine an arrival cost that has a weight based on previouslyestimated states and parameters.
 13. The battery management system ofclaim 12, wherein determine the arrival cost includes instructions that,when executed by the processor, cause the battery management system todetermine the arrival cost using a Kalman Filter when the battery systemis a linear unconstrained system.
 14. The battery management system ofclaim 12, wherein determine the arrival cost includes instructions that,when executed by the processor, cause the battery management system tolinearize the battery system when the battery system is a non-linearconstrained system; and determine a time varying arrival cost gain foreach parameter based on a estimation robustness of each parameter usinga modified extended Kalman Filter.
 15. The battery management system ofclaim 11, wherein the at least one state of the at least one batterycell includes at least one of a state-of-charge or a state-of-health ofthe at least one battery cell.
 16. The battery management system ofclaim 15, wherein estimate the at least one state of the at least onebattery cell by applying the electrochemical-based battery modelincludes instructions that, when executed by the processor, cause thebattery management system to synchronously estimate the state-of-chargeand the state-of-health of the at least one battery cell.
 17. Thebattery management system of claim 15, wherein estimate the at least onestate of the at least one battery cell by applying theelectrochemical-based battery model includes instructions that, whenexecuted by the processor, cause the battery management system toseparately estimate the state-of-charge and the state-of-health of theat least one battery cell, wherein the state-of-charge of the at leastone battery cell is estimated continuously, and wherein thestate-of-health of the at least one battery cell is estimated at apre-defined time.
 18. The battery management system of claim 17, whereinthe pre-defined time is one hundred drive cycles of a vehicle.
 19. Thebattery management system of claim 11, further comprising instructionsthat, when executed by the processor, cause the battery managementsystem to suspend the estimation of the at least one state of the atleast one battery cell under a low input persistency of excitation orunder a low gradient of output.
 20. The battery management system ofclaim 11, wherein the electrochemical-based battery model is aReduced-Order-Model of a Newman model.